What fraction of a given sample of a radioactive nuclide remains after four half-lives?

1 Answer
Jun 25, 2016

Answer:

It is #1/16# of the original population.

Explanation:

At the beginning you have that the number of atoms is #N_0#.
After the first half lives you have #N_1=N_0/2# because by definition the half life is that time where half of the sample had the decay.
After the second half life you have #N_2=N_1/2=N_0/4#.
As you can see, after each lifetime you divide by two the original population, then after four times you divide four times for #2# that means that you divide by #2^4=16#.
So the final population #N_4=N_0/16#.